In my experiences the accelerometer is pretty twitchy. What I mean is the value you get jumps around quiet a bit when you hold it steady in your hand and it's accurate enough to detect and count footsteps when the phone is in your pocket. Weather or not this is accurate enough for your needs will depend on the device.
It seems like a good candidate for a prototype. If it were me I would write a quick app that just displays the raw data from the accelerometer and test it out on a good elevator and a bad one to determine if it's feasible with the devices capabilities. I'm inclined to think it won't be accurate enough for tiny vibrations but I've underestimated how good these mobile sensors are before.
Take a look at Sensor Overviews
and be aware that different devices have different sensors.